Pentakis snub dodecahedron

Pentakis snub dodecahedron
Type	Conway polyhedron
Faces	140 triangles
Edges	210
Vertices	72
Vertex configurations	(12) 35 (60) 36
Symmetry group	Icosahedral (I)
Dual polyhedron	Truncated pentagonal hexecontahedron
Properties	convex, chiral
Net	(click to enlarge)

The pentakis snub dodecahedron is a convex polyhedron with 140 triangular faces, 210 edges, and 72 vertices. Like the snub dodecahedron, it has chiral icosahedral symmetry.

Its name comes from a topological construction from the snub dodecahedron with the kis operator applied to the pentagonal faces. In this construction, all the vertices are computed to be the same distance from the center. The 80 of the triangles are equilateral, and 60 triangles from the pentagons are isosceles.

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5
  • Chapter 21: Naming the Archimedean and Catalan polyhedra and Tilings (p 284)

External links

• Pentakis snub dodecahedron
• VTML polyhedral generator Try "k5sD" (Conway polyhedron notation)